Answer
396.9k+ views
Hint: Here, we will use the concept of the lines and angles of geometry. The sides and angles are generally known as part of any shape. So by calculating the maximum number of exterior angles a polygon can have we will get the number of acute angles a convex polygon can have.
Complete step by step solution:
It is given that the figure is a convex polygon which is a closed plane figure which is defined as the two dimensional figure which is lying on a single plane. Line segments are used to form a figure which is also known as the edges of the figure. The points at which these edges meet are known as the vertices of the figure.
Figures are generally known as polygons and these polygons generally vary according to the number of the edges of the figure.
So if a polygon has an interior acute angle which means that its corresponding exterior angle is greater than \[90^\circ \].
So, if a polygon has four sides or more than four sides which mean that the sum of the exterior angle will be greater than \[360^\circ \] which is not possible because the sum of all the exterior angle of a polygon must be equal to \[360^\circ \].
Therefore, a polygon can have a maximum of three acute angles in it.
Hence, maximum of three acute angles a convex polygon can have.
Note:
Geometry is the branch of mathematics that deals with points, lines and shapes. A triangle is a polygon with three edges/sides and three vertices. Side is one of the straight line segments which is used to construct/draw a polygon. When two or more lines cross each other in a plane, they are called intersecting lines and the point where these lines intersect is called a Point of Intersection.
Complete step by step solution:
It is given that the figure is a convex polygon which is a closed plane figure which is defined as the two dimensional figure which is lying on a single plane. Line segments are used to form a figure which is also known as the edges of the figure. The points at which these edges meet are known as the vertices of the figure.
Figures are generally known as polygons and these polygons generally vary according to the number of the edges of the figure.
So if a polygon has an interior acute angle which means that its corresponding exterior angle is greater than \[90^\circ \].
So, if a polygon has four sides or more than four sides which mean that the sum of the exterior angle will be greater than \[360^\circ \] which is not possible because the sum of all the exterior angle of a polygon must be equal to \[360^\circ \].
Therefore, a polygon can have a maximum of three acute angles in it.
Hence, maximum of three acute angles a convex polygon can have.
Note:
Geometry is the branch of mathematics that deals with points, lines and shapes. A triangle is a polygon with three edges/sides and three vertices. Side is one of the straight line segments which is used to construct/draw a polygon. When two or more lines cross each other in a plane, they are called intersecting lines and the point where these lines intersect is called a Point of Intersection.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)